Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.
$$5\sqrt{3}+3\times 2\sqrt{3}-\sqrt{48}$$
Multiply $3$ and $2$ to get $6$.
$$5\sqrt{3}+6\sqrt{3}-\sqrt{48}$$
Combine $5\sqrt{3}$ and $6\sqrt{3}$ to get $11\sqrt{3}$.
$$11\sqrt{3}-\sqrt{48}$$
Factor $48=4^{2}\times 3$. Rewrite the square root of the product $\sqrt{4^{2}\times 3}$ as the product of square roots $\sqrt{4^{2}}\sqrt{3}$. Take the square root of $4^{2}$.
$$11\sqrt{3}-4\sqrt{3}$$
Combine $11\sqrt{3}$ and $-4\sqrt{3}$ to get $7\sqrt{3}$.
